Hours per week – 2. semester:
Content (Syllabus outline)

Seminar leader prepares a sufficient number of short independent topics from different areas of mathematics suitable for students after completing three semesters of study. Topics are handed out to students along with necessary literature during the first meeting of the seminar. The handouts have to suffice for the preparation of the seminar, however students can look for additional sources.


gradivo, ki ga pripravi vodja seminarja
S. Krantz: A primer of mathematical writing, American Mathematical Society, 1997.

Objectives and competences

The purpose of the course is to teach a student how to prepare a presentation of a mathematical topic and how to write a mathematical text. As a part of the course the student will based on own experience, observing peers, and feedback information given by the seminar leader acquire the ability to prepare effective and understandable presentation of mathematical ideas (appropriate slides, intelligible explanations, organized board work, clearly written and structured seminar work).

Intended learning outcomes

Knowledge and understanding: Student learns to prepare a short presentation and to write a seminar paper.
Application: Gained experience will be of use during the course of study for other courses and later for work.
Reflection: The ability to connect new skills to the expertise.
Transferable skills: Gained experience will be of use during the course of study for other courses that require presentation or homework.

Learning and teaching methods

Student prepares a presentation in the duration of 60 minutes which is followed by a discussion and question session. The emphasis is not on the difficulty of the topic but rather on the clear and well structured presentation of ideas. The presentation has to be prepared in a way that the colleagues in the class can follow. The same criterion holds for the seminar work which has to be a self-contained presentation of the topic.


seminar work.
Grading: 6-10 pass, 5 fail (according to the rules of University of Ljubljana)

Lecturer's references

Tomaž Košir:
GRUNENFELDER, Luzius, KOŠIR, Tomaž. Koszul cohomology for finite families of comudule maps end applications. Communications in algebra, ISSN 0092-7872, 1997, let. 25, št. 2, str. 459-479. [COBISS-SI-ID 7127641]
GRUNENFELDER, Luzius, KOŠIR, Tomaž, OMLADIČ, Matjaž, RADJAVI, Heydar. On groups generated by elements of prime order. Geometriae dedicata, ISSN 0046-5755, 1999, let. 75, št. 3, str. 317-332. [COBISS-SI-ID 8849241]
GRUNENFELDER, Luzius, KOŠIR, Tomaž. On a representation of commuting maps by tensor product. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 1997, let. 251, str. 215-222. [COBISS-SI-ID 7104345]
George Mejak:
MEJAK, George. Eshebly tensors for a finite spherical domain with an axisymmetric inclusion. European journal of mechanics. A, Solids, ISSN 0997-7538. [Print ed.], 2011, vol. 30, iss. 4, str. 477-490. [COBISS-SI-ID 16025177]
MEJAK, George. Optimization of cross-section of hollow prismatic bars in torsion. Communications in numerical methods in engineering, ISSN 1069-8299, 2000, vol. 16, št. 10, str. 687-695. [COBISS-SI-ID 9984089]
MEJAK, George. Finite element solution of a model free surface problem by the optimal shape design approach. International journal for numerical methods in engineering, ISSN 0029-5981. [Print ed.], 1997, vol. 40, str. 1525-1550. [COBISS-SI-ID 9983833]
Bor Plestenjak:
PLESTENJAK, Bor. Numerical methods for the tridiagonal hyperbolic quadratic eigenvalue problem. V: Fifth international workshop on accurate solution in eigenvalue problems : hagen, Germany from June 29 to July 1, 2004. Philadelphia: SIAM, 2006, vol. 28, no. 4, str. 1157-1172. [COBISS-SI-ID 14367833]
HOCHSTENBACH, Michiel E., KOŠIR, Tomaž, PLESTENJAK, Bor. A Jacobi-Davidson type method for the two-parameter eigenvalue problem. SIAM journal on matrix analysis and applications, ISSN 0895-4798, 2005, vol. 26, no. 2, str. 477-497. [COBISS-SI-ID 13613401]
HOCHSTENBACH, Michiel E., PLESTENJAK, Bor. Backward error, condition numbers, and pseudospectra for the multiparamerer eigenvalue problem. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2003, vol. 375, str. 63-81. [COBISS-SI-ID 12778841]
Pavle Saksida:
SAKSIDA, Pavle. On zero-curvature condition and Fourier analysis. Journal of physics. A, Mathematical and theoretical, ISSN 1751-8113, 2011, vol. 44, no. 8, 085203 (19 str.). [COBISS-SI-ID 15909465]
SAKSIDA, Pavle. Lattices of Neumann oscillators and Maxwell-Bloch equations. Nonlinearity, ISSN 0951-7715, 2006, vol. 19, no. 3, str. 747-768. [COBISS-SI-ID 13932377]
SAKSIDA, Pavle. Nahm's equations and generalizations Neumann system. Proceedings of the London Mathematical Society, ISSN 0024-6115, 1999, let. 78, št. 3, str. 701-720. [COBISS-SI-ID 8853849]
Sašo Strle:
OWENS, Brendan, STRLE, Sašo. Rational homology spheres and the four-ball genus of knots. Advances in mathematics, ISSN 0001-8708, 2006, vol. 200, iss. 1, str. 196-216. [COBISS-SI-ID 13875033]
STRLE, Sašo. Bounds on genus and geometric intersections from cylindrical end moduli spaces. Journal of differential geometry, ISSN 0022-040X, 2003, vol. 65, no. 3, str. 469-511. [COBISS-SI-ID 13135193]
RUBERMAN, Daniel, STRLE, Sašo. Mod 2 Seiberg-Witten invariants of homology tori. Mathematical research letters, ISSN 1073-2780, 2000, vol. 7, no. 5-6, str. 789-799. [COBISS-SI-ID 10557785]